GCF of 42/68, 141/13, 491/440
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 42/68, 141/13, 491/440 i.e 1/97240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/68, 141/13, 491/440.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 42/68,141/13,491/440?
Given fractions are 42/68,141/13,491/440
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 42/68,141/13,491/440, numerators are 42,141,491
Denominators are 68,13,440
The GCF of 42,141,491 is 1 .
LCM of 68,13,440 is 97240.
The greatest common factor of 42/68,141/13,491/440 = [GCF of 42,141,491]/[LCM of 68,13,440]= 1/97240
Therefore, the GCF of 42/68,141/13,491/440 is 1/97240.
To find the highest common factor of 42,141,491, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 141 are 1, 3, 47, 141
The factors of 491 are 1, 491
The HCF of 42,141,491 is 1.
Lets's calculate GCF of 42,141,491
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 42,141,491 By Matching Biggest Common Factor Method
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 141
:1,3,47,141
Now, list down the factors of 491
:1,491
Greatest Common Factor
We found the factors 42,141,491 . The biggest common factor number is the GCF number.
So the greatest common factor 42,141,491 is 1.
Lets's calculate LCM of 68,13,440
| 2 | 68, 13, 440 |
| 2 | 34, 13, 220 |
| 17, 13, 110 |
∴ So the LCM of the given numbers is 2 x 2 x 17 x 13 x 110 = 97240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/97240
Therefore, the GCF of Fractions 42/68,141/13,491/440 is 1/97240
Least Common Multiple of 68,13,440 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 68,13,440 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,13,440) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(68,13,440) x common factors =1 x 4 = 4
LCM(68,13,440) = ( 68 × 13 × 440 ) / 4
LCM(68,13,440) = 388960 / 4
LCM(68,13,440) = 97240
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FAQs on GCF of Fractions of 42/68, 141/13, 491/440
1. What is the HCF of 42,141,491?
The HCF of 42,141,491 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 42/68, 141/13, 491/440?
Answer: GCF of Numerators as per given numbers 42/68, 141/13, 491/440 is
GCF of Numerators i.e. for 42,141,491 is 1
LCM of denominators i.e. for 68,13,440 is 97240.
Thus, GCF of Fractions is 1/97240.Finally, GCF of Fractions for 42/68, 141/13, 491/440 is 1/97240.